Fatou Julia Montel

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Fatou, Julia, Montel

Michèle Audin
Fatou Julia Montel Book PDF

Author : Michèle Audin
Publisher : Springer Science & Business Media
Page : 342 pages
File Size : 47,9 Mb
Release : 2011-01-30
Category : Mathematics
ISBN : 9783642178535

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Fatou, Julia, Montel by Michèle Audin Pdf

How did Pierre Fatou and Gaston Julia create what we now call Complex Dynamics, in the context of the early twentieth century and especially of the First World War? The book is based partly on new, unpublished sources. Who were Pierre Fatou, Gaston Julia, Paul Montel? New biographical information is given on the little known mathematician that was Pierre Fatou. How did the WW1 injury of Julia influence mathematical life in France? From the reviews of the French version: "Audin’s book is ... filled with marvelous biographical information and analysis, dealing not just with the men mentioned in the book’s title but a large number of other players, too ... [It] addresses itself to scholars for whom the history of mathematics has a particular resonance and especially to mathematicians active, or even with merely an interest, in complex dynamics. ... presents it all to the reader in a very appealing form." (Michael Berg, The Mathematical Association of America, October 2009)

Fractals and Chaos

Benoit Mandelbrot
Fractals and Chaos Book PDF

Author : Benoit Mandelbrot
Publisher : Springer Science & Business Media
Page : 321 pages
File Size : 52,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475740172

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Fractals and Chaos by Benoit Mandelbrot Pdf

Just 23 years ago Benoit Mandelbrot published his famous picture of the Mandelbrot set, but that picture has changed our view of the mathematical and physical universe. In this text, Mandelbrot offers 25 papers from the past 25 years, many related to the famous inkblot figure. Of historical interest are some early images of this fractal object produced with a crude dot-matrix printer. The text includes some items not previously published.

Fractals, Wavelets, and their Applications

Christoph Bandt,Michael Barnsley,Robert Devaney,Kenneth J. Falconer,V. Kannan,Vinod Kumar P.B.
Fractals Wavelets and their Applications Book PDF

Author : Christoph Bandt,Michael Barnsley,Robert Devaney,Kenneth J. Falconer,V. Kannan,Vinod Kumar P.B.
Publisher : Springer
Page : 508 pages
File Size : 52,8 Mb
Release : 2014-09-27
Category : Mathematics
ISBN : 9783319081052

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Fractals, Wavelets, and their Applications by Christoph Bandt,Michael Barnsley,Robert Devaney,Kenneth J. Falconer,V. Kannan,Vinod Kumar P.B. Pdf

Fractals and wavelets are emerging areas of mathematics with many common factors which can be used to develop new technologies. This volume contains the selected contributions from the lectures and plenary and invited talks given at the International Workshop and Conference on Fractals and Wavelets held at Rajagiri School of Engineering and Technology, India from November 9-12, 2013. Written by experts, the contributions hope to inspire and motivate researchers working in this area. They provide more insight into the areas of fractals, self similarity, iterated function systems, wavelets and the applications of both fractals and wavelets. This volume will be useful for the beginners as well as experts in the fields of fractals and wavelets.

A History of Complex Dynamics

Daniel S. Alexander
A History of Complex Dynamics Book PDF

Author : Daniel S. Alexander
Publisher : Springer Science & Business Media
Page : 175 pages
File Size : 42,6 Mb
Release : 2013-06-29
Category : Technology & Engineering
ISBN : 9783663091974

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A History of Complex Dynamics by Daniel S. Alexander Pdf

The contemporary study of complex dynamics, which has flourished so much in recent years, is based largely upon work by G. Julia (1918) and P. Fatou (1919/20). The goal of this book is to analyze this work from an historical perspective and show in detail, how it grew out of a corpus regarding the iteration of complex analytic functions. This began with investigations by E. Schröder (1870/71) which he made, when he studied Newton's method. In the 1880's, Gabriel Koenigs fashioned this study into a rigorous body of work and, thereby, influenced a lot the subsequent development. But only, when Fatou and Julia applied set theory as well as Paul Montel's theory of normal families, it was possible to develop a global approach to the iteration of rational maps. This book shows, how this intriguing piece of modern mathematics became reality.

Toeplitz Matrices and Operators

Nikolaï Nikolski
Toeplitz Matrices and Operators Book PDF

Author : Nikolaï Nikolski
Publisher : Cambridge University Press
Page : 453 pages
File Size : 48,6 Mb
Release : 2020-01-02
Category : Mathematics
ISBN : 9781107198500

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Toeplitz Matrices and Operators by Nikolaï Nikolski Pdf

A friendly introduction to Toeplitz theory and its applications throughout modern functional analysis.

Hidden Harmony—Geometric Fantasies

Umberto Bottazzini,Jeremy Gray
Hidden Harmony Geometric Fantasies Book PDF

Author : Umberto Bottazzini,Jeremy Gray
Publisher : Springer Science & Business Media
Page : 860 pages
File Size : 43,6 Mb
Release : 2013-06-21
Category : Mathematics
ISBN : 9781461457251

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Hidden Harmony—Geometric Fantasies by Umberto Bottazzini,Jeremy Gray Pdf

​This book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject – Cauchy, Riemann, and Weierstrass – it looks at the contributions of authors from d’Alembert to Hilbert, and Laplace to Weyl. Particular chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been devoted to the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. The book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main actors lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions. The book is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It documents the motivations for the early ideas and their gradual refinement into a rigorous theory.​

The Map and the Territory

Shyam Wuppuluri,Francisco Antonio Doria
The Map and the Territory Book PDF

Author : Shyam Wuppuluri,Francisco Antonio Doria
Publisher : Springer
Page : 641 pages
File Size : 42,9 Mb
Release : 2018-02-13
Category : Science
ISBN : 9783319724782

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The Map and the Territory by Shyam Wuppuluri,Francisco Antonio Doria Pdf

This volume presents essays by pioneering thinkers including Tyler Burge, Gregory Chaitin, Daniel Dennett, Barry Mazur, Nicholas Humphrey, John Searle and Ian Stewart. Together they illuminate the Map/Territory Distinction that underlies at the foundation of the scientific method, thought and the very reality itself. It is imperative to distinguish Map from the Territory while analyzing any subject but we often mistake map for the territory. Meaning for the Reference. Computational tool for what it computes. Representations are handy and tempting that we often end up committing the category error of over-marrying the representation with what is represented, so much so that the distinction between the former and the latter is lost. This error that has its roots in the pedagogy often generates a plethora of paradoxes/confusions which hinder the proper understanding of the subject. What are wave functions? Fields? Forces? Numbers? Sets? Classes? Operators? Functions? Alphabets and Sentences? Are they a part of our map (theory/representation)? Or do they actually belong to the territory (Reality)? Researcher, like a cartographer, clothes (or creates?) the reality by stitching multitudes of maps that simultaneously co-exist. A simple apple, for example, can be analyzed from several viewpoints beginning with evolution and biology, all the way down its microscopic quantum mechanical components. Is there a reality (or a real apple) out there apart from these maps? How do these various maps interact/intermingle with each other to produce a coherent reality that we interact with? Or do they not? Does our brain uses its own internal maps to facilitate “physicist/mathematician” in us to construct the maps about the external territories in turn? If so, what is the nature of these internal maps? Are there meta-maps? Evolution definitely fences our perception and thereby our ability to construct maps, revealing to us only those aspects beneficial for our survival. But the question is, to what extent? Is there a way out of the metaphorical Platonic cave erected around us by the nature? While “Map is not the territory” as Alfred Korzybski remarked, join us in this journey to know more, while we inquire on the nature and the reality of the maps which try to map the reality out there. The book also includes a foreword by Sir Roger Penrose and an afterword by Dagfinn Follesdal.

Transcendence in Algebra, Combinatorics, Geometry and Number Theory

Alin Bostan,Kilian Raschel
Transcendence in Algebra Combinatorics Geometry and Number Theory Book PDF

Author : Alin Bostan,Kilian Raschel
Publisher : Springer Nature
Page : 544 pages
File Size : 53,9 Mb
Release : 2021-11-02
Category : Mathematics
ISBN : 9783030843045

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Transcendence in Algebra, Combinatorics, Geometry and Number Theory by Alin Bostan,Kilian Raschel Pdf

This proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Brașov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees.

Mathematics Without Boundaries

Themistocles M. Rassias,Panos M. Pardalos
Mathematics Without Boundaries Book PDF

Author : Themistocles M. Rassias,Panos M. Pardalos
Publisher : Springer
Page : 783 pages
File Size : 45,7 Mb
Release : 2014-09-17
Category : Mathematics
ISBN : 9781493911066

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Mathematics Without Boundaries by Themistocles M. Rassias,Panos M. Pardalos Pdf

The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the latest information.

A Century of Advancing Mathematics

Paul Zorn
A Century of Advancing Mathematics Book PDF

Author : Paul Zorn
Publisher : The Mathematical Association of America
Page : 436 pages
File Size : 55,5 Mb
Release : 2015-08-23
Category : Mathematics
ISBN : 9780883855881

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A Century of Advancing Mathematics by Paul Zorn Pdf

The MAA was founded in 1915 to serve as a home for The American Mathematical Monthly. The mission of the Association-to advance mathematics, especially at the collegiate level-has, however, always been larger than merely publishing world-class mathematical exposition. MAA members have explored more than just mathematics; we have, as this volume tries to make evident, investigated mathematical connections to pedagogy, history, the arts, technology, literature, every field of intellectual endeavor. Essays, all commissioned for this volume, include exposition by Bob Devaney, Robin Wilson, and Frank Morgan; history from Karen Parshall, Della Dumbaugh, and Bill Dunham; pedagogical discussion from Paul Zorn, Joe Gallian, and Michael Starbird, and cultural commentary from Bonnie Gold, Jon Borwein, and Steve Abbott. This volume contains 35 essays by all-star writers and expositors writing to celebrate an extraordinary century for mathematics-more mathematics has been created and published since 1915 than in all of previous recorded history. We've solved age-old mysteries, created entire new fields of study, and changed our conception of what mathematics is. Many of those stories are told in this volume as the contributors paint a portrait of the broad cultural sweep of mathematics during the MAA's first century. Mathematics is the most thrilling, the most human, area of intellectual inquiry; you will find in this volume compelling proof of that claim.

Early Days in Complex Dynamics

Daniel S. Alexander,Felice Iavernaro,Alessandro Rosa
Early Days in Complex Dynamics Book PDF

Author : Daniel S. Alexander,Felice Iavernaro,Alessandro Rosa
Publisher : American Mathematical Soc.
Page : 474 pages
File Size : 45,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821844649

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Early Days in Complex Dynamics by Daniel S. Alexander,Felice Iavernaro,Alessandro Rosa Pdf

The theory of complex dynamics, whose roots lie in 19th-century studies of the iteration of complex function conducted by Koenigs, Schoder, and others, flourished remarkably during the first half of the 20th century, when many of the central ideas and techniques of the subject developed. This book paints a robust picture of the field of complex dynamics between 1906 and 1942 through detailed discussions of the work of Fatou, Julia, Siegel, and several others.

Polynomial Root-finding and Polynomiography

Bahman Kalantari
Polynomial Root finding and Polynomiography Book PDF

Author : Bahman Kalantari
Publisher : World Scientific
Page : 492 pages
File Size : 52,8 Mb
Release : 2009
Category : Computers
ISBN : 9789812700599

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Polynomial Root-finding and Polynomiography by Bahman Kalantari Pdf

This book offers fascinating and modern perspectives into the theory and practice of the historical subject of polynomial root-finding, rejuvenating the field via polynomiography, a creative and novel computer visualization that renders spectacular images of a polynomial equation. Polynomiography will not only pave the way for new applications of polynomials in science and mathematics, but also in art and education. The book presents a thorough development of the basic family, arguably the most fundamental family of iteration functions, deriving many surprising and novel theoretical and practical applications such as: algorithms for approximation of roots of polynomials and analytic functions, polynomiography, bounds on zeros of polynomials, formulas for the approximation of Pi, and characterizations or visualizations associated with a homogeneous linear recurrence relation. These discoveries and a set of beautiful images that provide new visions, even of the well-known polynomials and recurrences, are the makeup of a very desirable book. This book is a must for mathematicians, scientists, advanced undergraduates and graduates, but is also for anyone with an appreciation for the connections between a fantastically creative art form and its ancient mathematical foundations.

The God Problem

Howard Bloom
The God Problem Book PDF

Author : Howard Bloom
Publisher : Prometheus Books
Page : 714 pages
File Size : 55,6 Mb
Release : 2012-08-30
Category : Religion
ISBN : 9781616145521

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The God Problem by Howard Bloom Pdf

God’s war crimes, Aristotle’s sneaky tricks, Einstein’s pajamas, information theory’s blind spot, Stephen Wolfram’s new kind of science, and six monkeys at six typewriters getting it wrong. What do these have to do with the birth of a universe and with your need for meaning? Everything, as you’re about to see. How does the cosmos do something it has long been thought only gods could achieve? How does an inanimate universe generate stunning new forms and unbelievable new powers without a creator? How does the cosmos create? That’s the central question of this book, which finds clues in strange places. Why A does not equal A. Why one plus one does not equal two. How the Greeks used kickballs to reinvent the universe. And the reason that Polish-born Benoît Mandelbrot—the father of fractal geometry—rebelled against his uncle. You’ll take a scientific expedition into the secret heart of a cosmos you’ve never seen. Not just any cosmos. An electrifyingly inventive cosmos. An obsessive-compulsive cosmos. A driven, ambitious cosmos. A cosmos of colossal shocks. A cosmos of screaming, stunning surprise. A cosmos that breaks five of science’s most sacred laws. Yes, five. And you’ll be rewarded with author Howard Bloom’s provocative new theory of the beginning, middle, and end of the universe—the Bloom toroidal model, also known as the big bagel theory—which explains two of the biggest mysteries in physics: dark energy and why, if antimatter and matter are created in equal amounts, there is so little antimatter in this universe. Called "truly awesome" by Nobel Prize–winner Dudley Herschbach, The God Problem will pull you in with the irresistible attraction of a black hole and spit you out again enlightened with the force of a big bang. Be prepared to have your mind blown. From the Hardcover edition.

Mathematics across the Iron Curtain

Christopher Hollings
Mathematics across the Iron Curtain Book PDF

Author : Christopher Hollings
Publisher : American Mathematical Society
Page : 457 pages
File Size : 43,5 Mb
Release : 2014-07-16
Category : Mathematics
ISBN : 9781470414931

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Mathematics across the Iron Curtain by Christopher Hollings Pdf

The theory of semigroups is a relatively young branch of mathematics, with most of the major results having appeared after the Second World War. This book describes the evolution of (algebraic) semigroup theory from its earliest origins to the establishment of a full-fledged theory. Semigroup theory might be termed `Cold War mathematics' because of the time during which it developed. There were thriving schools on both sides of the Iron Curtain, although the two sides were not always able to communicate with each other, or even gain access to the other's publications. A major theme of this book is the comparison of the approaches to the subject of mathematicians in East and West, and the study of the extent to which contact between the two sides was possible.

The War of Guns and Mathematics

David Aubin,Catherine Goldstein
The War of Guns and Mathematics Book PDF

Author : David Aubin,Catherine Goldstein
Publisher : American Mathematical Society
Page : 414 pages
File Size : 50,7 Mb
Release : 2014-10-07
Category : Mathematics
ISBN : 9781470414696

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The War of Guns and Mathematics by David Aubin,Catherine Goldstein Pdf

For a long time, World War I has been shortchanged by the historiography of science. Until recently, World War II was usually considered as the defining event for the formation of the modern relationship between science and society. In this context, the effects of the First World War, by contrast, were often limited to the massive deaths of promising young scientists. By focusing on a few key places (Paris, Cambridge, Rome, Chicago, and others), the present book gathers studies representing a broad spectrum of positions adopted by mathematicians about the conflict, from militant pacifism to military, scientific, or ideological mobilization. The use of mathematics for war is thoroughly examined. This book suggests a new vision of the long-term influence of World War I on mathematics and mathematicians. Continuities and discontinuities in the structure and organization of the mathematical sciences are discussed, as well as their images in various milieux. Topics of research and the values with which they were defended are scrutinized. This book, in particular, proposes a more in-depth evaluation of the issue of modernity and modernization in mathematics. The issue of scientific international relations after the war is revisited by a close look at the situation in a few Allied countries (France, Britain, Italy, and the USA). The historiography has emphasized the place of Germany as the leading mathematical country before WWI and the absurdity of its postwar ostracism by the Allies. The studies presented here help explain how dramatically different prewar situations, prolonged interaction during the war, and new international postwar organizations led to attempts at redrafting models for mathematical developments.